Chen and Yan (1989) presented a result on zero crossings of boundary curvature under morphological openings. In this correspondence, it is shown, by means of a counter example, that this result is not correct. An analysis of the counter example shows where Chen and Yan go wrong and determines a class of images for which their theorem holds.>

This correspondence presents a metric for describing line segments. This metric measures how well two line segments can be replaced by a single longer one. This depends for example on collinearity and nearness of the line segments. The metric is constructed using a new technique using so-called neighborhood functions. The behavior of the metric depends on the neighborhood function chosen. In this correspondence, an appropriate choice for the case of line segments is presented. The quality of the metric is verified by using it in a simple clustering algorithm that groups line segments found by an edge detection algorithm in an image. The fact that the clustering algorithm can detect long linear structures in an image shows that the metric is a good measure for the groupability of line segments.>